Question

C. why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?
a. since the distribution is of sample​ means, not​ individuals, the distribution is a normal distribution for any sample size.
b. since the mean pulse rate exceeds​ 30, the distribution of sample means is a normal distribution for any sample size.
c. since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.
d. since the distribution is of​ individuals, not sample​ means, the distribution is a normal distribution for any sample size.

Answer 1

I think it’s c but I’m not 100% sure

Answer 2

According to the Central Limit Theorem, the correct option is:

c. since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

• The Central Limit Theorem establishes that, for a normally distributed random variable X with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n is approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

• For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem:

• When the underlying distribution is normal, the Central Limit Theorem holds for any sample size, thus, the correct option is c.

A similar problem is given at https://brainly.com/question/14099217